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Practice Class 8 Maths Chapter 4 Practical Geometry MCQ Questions with Answers and Solutions based on NCERT concepts. Solve fresh questions on quadrilateral construction, diagonals, angles, circles, and geometrical instruments.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 8
Difficulty Level: Difficult
Based On: NCERT Mathematics
Introduction
Practical Geometry requires students to carefully interpret the measurements given for a geometrical figure. In quadrilateral construction, different combinations of sides, angles, and diagonals can provide enough information to determine the required figure.
Students must also understand how construction tools work together. A ruler helps construct lengths, a protractor helps construct angles, and a compass helps transfer lengths and draw arcs.
This Practice Set 8 contains 5 fresh MCQs focusing on construction reasoning, angle relationships, diagonals, and the correct use of geometrical instruments.
What You Will Learn
✔ Identifying suitable construction information
✔ Understanding relationships between sides and angles
✔ Using a diagonal during construction
✔ Applying compass and protractor concepts
✔ Verifying construction conditions
✔ Solving application-based geometry questions
Why This Topic Is Important
Practical Geometry strengthens students’ understanding of how geometrical figures are formed from specific conditions. It develops accuracy, visualisation, logical reasoning, and practical mathematical skills.
These concepts are useful in school examinations as well as higher-level geometry.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ NCERT-Based Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Mathematics Revision
✔ Geometry Practice
Q1. A quadrilateral is to be constructed when three sides and two diagonals are known. What is the main purpose of the diagonal information?
A) It helps determine the positions of the vertices
B) It changes the quadrilateral into a circle
C) It gives the colour of the figure
D) It determines only the perimeter
Answer:
A) It helps determine the positions of the vertices
Useful Concept
Diagonals provide additional distance information that can help locate vertices and determine the shape of a quadrilateral.
Solution
Suppose a quadrilateral has vertices:
$$ABCD$$
and its diagonals:
$$AC$$
and:
$$BD$$
are known.
These diagonals connect opposite vertices and provide additional measurements about the positions of those vertices.
Together with the given side information, they can help determine the required construction.
Therefore, the diagonal information helps determine the positions of the vertices.
Hence, the correct answer is:
A) It helps determine the positions of the vertices
Q2. If two sides of a triangle are $$6\text{ cm}$$ and $$8\text{ cm}$$ and the included angle is $$90^\circ$$, which instrument is needed to construct the angle accurately?
A) Compass
B) Protractor
C) Ruler only
D) Divider
Answer:
B) Protractor
Useful Concept
A protractor is used to construct an angle of a specified measure.
Solution
The given angle is:
$$90^\circ$$
Since an exact angle must be constructed, a protractor can be used to mark:
$$90^\circ$$
from the given side.
After constructing the angle, the second side can be marked with the given length.
Therefore, the required instrument is:
B) Protractor
Q3. A student needs to locate a point $$D$$ such that:
$$AD=5\text{ cm}$$
and:
$$BD=4\text{ cm}$$
from two known points $$A$$ and $$B$$. Which method is suitable for locating $$D$$?
A) Draw two arcs with centres $$A$$ and $$B$$
B) Draw only one straight line
C) Measure only one angle
D) Draw a random circle
Answer:
A) Draw two arcs with centres $$A$$ and $$B$$
Useful Concept
A point at specified distances from two known points can be located using intersecting arcs.
Solution
The required distances are:
$$AD=5\text{ cm}$$
and:
$$BD=4\text{ cm}$$
To locate $$D$$:
- Draw an arc with centre $$A$$ and radius $$5\text{ cm}$$.
- Draw another arc with centre $$B$$ and radius $$4\text{ cm}$$.
- The intersection of the two arcs gives the possible position of $$D$$.
Thus, intersecting arcs are the appropriate construction method.
Hence, the correct answer is:
A) Draw two arcs with centres $$A$$ and $$B$$
Q4. If two construction arcs intersect at two different points, what can this indicate?
A) There may be two possible positions satisfying the distance conditions
B) The construction is automatically impossible
C) Both points must be midpoints
D) The compass is always incorrect
Answer:
A) There may be two possible positions satisfying the distance conditions
Useful Concept
Two circles or arcs can intersect at two points. Both intersection points can satisfy the same distance conditions.
Solution
Suppose an arc centred at $$A$$ and another centred at $$B$$ are drawn with suitable radii.
If they intersect at two points:
$$C$$
and:
$$D$$
then both points may satisfy:
$$AC=AD$$
and:
$$BC=BD$$
for the respective radii.
Therefore, there can be two possible positions satisfying the distance conditions.
Hence, the correct answer is:
A) There may be two possible positions satisfying the distance conditions
Q5. A student constructs a quadrilateral but finds that one given diagonal is shorter than the sum of the two corresponding sides. What should the student do first?
A) Check the construction and measurements
B) Change the given data
C) Ignore the diagonal
D) Colour the quadrilateral
Answer:
A) Check the construction and measurements
Useful Concept
When a construction does not satisfy the given measurements, the first step is to verify the construction and check for measurement or instrument errors.
Solution
A construction should satisfy all the conditions specified in the question.
If the constructed diagonal does not match the expected geometrical relationship, the student should not change the original data.
Instead, the student should check:
✔ Side lengths
✔ Diagonal length
✔ Compass opening
✔ Construction points
✔ Measurement accuracy
Therefore, the appropriate first action is to check the construction and measurements.
Hence, the correct answer is:
A) Check the construction and measurements
Important Concepts
Locating a Point Using Two Distances
If a point $$D$$ must satisfy:
$$AD=5\text{ cm}$$
and:
$$BD=4\text{ cm}$$
two arcs can be used to locate it.
Intersecting Arcs
Two arcs can intersect at:
✔ One point
✔ Two points
✔ No point
depending on their centres and radii.
Two Possible Positions
If two arcs intersect at two points, both points may satisfy the required distance conditions.
Angle Construction
A specified angle such as:
$$90^\circ$$
can be constructed accurately using a protractor.
Checking Construction
If the completed figure does not satisfy the given conditions, check the measurements and construction steps before changing anything.
Related Practice Questions
Q1. If:
$$AC=5\text{ cm}$$
and:
$$BC=6\text{ cm}$$
are required, how can point $$C$$ be located?
Q2. How many points can two circles intersect at?
Q3. Which instrument is used to construct:
$$75^\circ$$
Q4. Why can two arcs produce two possible positions for a point?
Q5. What should be checked if the final construction does not satisfy the given measurements?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. A point is required to be:
$$4\text{ cm}$$
from $$P$$ and:
$$6\text{ cm}$$
from $$Q$$. What can be used to locate the point?
A) Two suitable arcs
B) Only a protractor
C) Only an eraser
D) Only a ruler without measurement
Q2. Two arcs may intersect at:
A) At most two points
B) Four points always
C) No possible points ever
D) Ten points always
Q3. Which instrument is suitable for constructing:
$$120^\circ$$
A) Protractor
B) Ruler only
C) Compass only
D) Pencil only
Q4. If a construction does not satisfy the given conditions, what should be done first?
A) Check the measurements and construction
B) Change the question
C) Ignore the error
D) Colour the figure
Q5. Two intersecting arcs can help determine:
A) A required point
B) The colour of a figure
C) The perimeter automatically
D) The area automatically
Exam Tips
✔ Identify all given distances before starting.
✔ Use separate arcs for separate distance conditions.
✔ Remember that two arcs can intersect at two possible points.
✔ Use a protractor when an exact angle is specified.
✔ Check the compass opening before drawing an arc.
✔ Verify the completed figure against every given condition.
✔ Never change the information given in the question to match an incorrect construction.
Quick Revision Notes
✔ A point at fixed distances from two points can be located using two arcs.
✔ Two circles or arcs may intersect at zero, one, or two points.
✔ Two intersection points can represent two possible positions.
✔ A protractor is used for specified angles.
✔ A compass is used for arcs and transferring lengths.
✔ Construction errors should be checked before changing any given measurement.
Common Mistakes Students Make
❌ Using incorrect radii for construction arcs.
❌ Assuming two arcs always have exactly one intersection.
❌ Forgetting that two intersection points can give two possible positions.
❌ Changing the given data instead of correcting the construction.
❌ Measuring an angle inaccurately.
❌ Failing to verify the completed quadrilateral.
Key Takeaways
✔ Construction depends on accurate measurements.
✔ Intersecting arcs can locate points satisfying two distance conditions.
✔ Two arcs may have two possible intersection points.
✔ Protractor is used for accurate angle construction.
✔ Construction should always be checked against the original conditions.
✔ Correct use of geometrical instruments is essential.
FAQs
Q. How can a point at two specified distances be located?
Answer:
Draw an arc with the first known point as centre and the first distance as radius. Then draw another arc with the second known point as centre and the second distance as radius. Their intersection gives the required point or possible points.
Q. Can two arcs intersect at two points?
Answer:
Yes. Depending on their centres and radii, two circles or arcs can intersect at two points.
Q. What should be done if a construction is incorrect?
Answer:
The measurements, compass settings, angles, and construction steps should be checked carefully before attempting the construction again.
Q. Which instrument is used to construct an exact angle?
Answer:
A protractor is used to measure and construct angles of specified measures.
Q. Why are diagonals useful in quadrilateral construction?
Answer:
Diagonals provide additional distance information and can divide a quadrilateral into triangles, making construction easier.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on locating points using arcs, angle construction, diagonal information, and checking geometrical constructions.
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